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Question 4 of 30 (1 point) I Question Attempt: 1 of 3
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Which type of error? Batteries used in a certain heart pacemaker have a mean life of 7 years. A new type of battery is being tested and will be used in place of the old battery if it can be shown to have a mean lifetime of more than 7 years. A test is made of versus . There are two possible errors. Identify them.
Part 1 of 2
(a) The true mean is 7 or less, but the new batteries are used.
This is a Type error.
Part:
Part 2 of 2
(b) The true mean is greater than 7, but the new batteries are not used.
This is a Type (Choose one) error.
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Studdy Solution
STEP 1
1. We are dealing with hypothesis testing.
2. The null hypothesis is that the mean lifetime of the new battery is 7 years.
3. The alternative hypothesis is that the mean lifetime of the new battery is greater than 7 years.
4. There are two types of errors in hypothesis testing: Type I and Type II errors.
STEP 2
1. Define Type I and Type II errors.
2. Identify the type of error for each scenario given.
STEP 3
Define Type I error:
A Type I error occurs when the null hypothesis is true, but we reject it.
STEP 4
Define Type II error:
A Type II error occurs when the null hypothesis is false, but we fail to reject it.
STEP 5
Identify the error in Part 1 of 2:
(a) The true mean is 7 or less, but the new batteries are used.
This is a Type I error because we are rejecting when it is true.
STEP 6
Identify the error in Part 2 of 2:
(b) The true mean is greater than 7, but the new batteries are not used.
This is a Type II error because we are failing to reject when it is false.
The identified errors are:
(a) Type I error
(b) Type II error
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